Microstructures for transforming light having lambertian distribution into batwing distributions

ABSTRACT

A light transmissive substrate for transforming a Lambertian light distribution into a batwing light distribution. The light transmissive substrate includes a first surface comprising a plurality of microstructures, and a second surface on a side of the substrate opposite the first surface. The substrate is configured to receive light in a Lambertian distribution from a light source at the first surface and transform the light into a batwing distribution exiting the second surface. The batwing distribution having a peak intensity at about ±30° to about ±60° from X and Y axes, and a minimum intensity at nadir.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application relies for priority on U.S. Provisional PatentApplication Ser. No. 62/623,894, entitled “MICROSTRUCTURES FORTRANSFORMING LIGHT HAVING LAMBERTIAN DISTRIBUTION INTO BATWINGDISTRIBUTIONS,” filed Jan. 30, 2018, the entire content of which ishereby incorporated by reference.

FIELD

The present invention is related to micro light transmitting optics andmicrostructures for transforming light having a Lambertian distributioninto batwing distributions for large area uniform illumination.

BACKGROUND

Light emitting diodes (LEDs) have quickly become the primary lightgenerating device for current applications. Intrinsically, an LED emitsthe light in a Lambertian distribution, characterized by the strongestintensity at the emitting direction (zero degrees or “nadir”). Lightintensity decreases following the cosine function of the angles deviatedfrom the zero-degree (nadir) emitting direction and reduces to zero asthe angle reaches 90 degrees from nadir, as illustrated in FIG. 1. Whenan LED is used to illuminate a flat surface target, the light travelingpath length varies for different target locations. Typically, the pathlength is the shortest at the zero-degree direction where the LED emitsthe highest light intensity, which forces designers to increase thelight source density to achieve a good illumination uniformity.

For applications that require uniform or even illumination over adesired area of a flat plane with low light source density, such as theback light units for displays or lighting projects for a large area, thelight source should deliver light energy in the reverse fashion of aLambertian distribution, i.e. reduced intensity at zero degrees (nadir)and high intensity at angles away from nadir, as shown in FIG. 2, forexample. Such a distribution profile (illustrated in FIG. 2) is oftenreferred as a “batwing” distribution and is more desirable for achievinguniform illumination.

Transforming a Lambertian distribution emitted by, for example, an LEDlight source into a batwing distribution may be achieved efficiently forsome applications, such as some lighting applications, by using bulkoptical lenses with specifically designed shapes. Such structures maynot be feasible for many applications in which LEDs are used, such as indisplays of cell phones, smart phones, tablets, laptop computers, etc.,due to the structure bulkiness of implanting such solutions. It isdesirable to transform a Lambertian distribution into a batwingdistribution with structures that are more compact than current opticallenses.

SUMMARY

It has been found that micro optical transmissive structures that arefabricated on a light transmissible substrate may be used to perform thedesired transformation functions to transform a Lambertian distributioninto a desired batwing distribution so that a substantially uniformillumination may be provided to a large area relative to the size of anLED light source. Embodiments of the present invention are describedbelow.

According to an aspect of the invention, there is provided a lighttransmissive substrate for transforming a Lambertian light distributioninto a batwing light distribution. The light transmissive substrateincludes a first surface comprising a plurality of microstructures, anda second surface on a side of the substrate opposite the first surface.The substrate is configured to receive light in a Lambertiandistribution from a light source at the first surface and transform thelight into a batwing distribution exiting the second surface. Thebatwing distribution has a peak intensity at about ±30° to about ±60°from X and Y axes and a minimum intensity at nadir.

In an embodiment, each of the plurality of microstructures has a shapeof a pyramid extending in a direction away from the second surface. Inan embodiment, at least the microstructures are made from materialhaving a refractive index of about 1.5, and the pyramid has a roof angleof between about 70° and about 95°.

In an embodiment, each pyramid has a base portion and a top portionconnected to the base portion. The top portion includes a tip of thepyramid and has sides disposed at different angles than sides of thebase portion.

In an embodiment, at least the microstructures are made from materialhaving a refractive index of about 1.5, the sides of the base portionare disposed at angles of about 55° relative to a plane substantiallyparallel to the second surface, and the top portion has a roof angle ofbetween about 85° and about 90°.

In an embodiment, each of the plurality of microstructures has a shapeof a frustum of a pyramid and a recess in a shape of a reverse pyramid.In an embodiment, at least the microstructures are made from materialhaving a refractive index of about 1.5, sides of the frustum aredisposed at angles of about 55° relative to a plane substantiallyparallel to the second surface, and the reverse pyramid has a roof angleof between about 85° and about 90°.

In an embodiment, each of the plurality of microstructures has a shapeof a corner cube.

In an embodiment, the second surface is substantially planar.

In an embodiment, the second surface comprises a texture.

These and other aspects, features, and characteristics of the presentinvention, as well as the methods of operation and functions of therelated elements of structure and the combination of parts and economiesof manufacture, will become more apparent upon consideration of thefollowing description and the appended claims with reference to theaccompanying drawings, all of which form a part of this specification.It is to be expressly understood, however, that the drawings are for thepurpose of illustration and description only and are not intended as adefinition of the limits of the invention. As used in the specificationand in the claims, the singular form of “a”, “an”, and “the” includeplural referents unless the context clearly dictates otherwise.

BRIEF DESCRIPTION OF THE DRAWINGS

The components of the following figures are illustrated to emphasize thegeneral principles of the present disclosure and are not necessarilydrawn to scale, although at least one of the figures may be drawn toscale. Reference characters designating corresponding components arerepeated as necessary throughout the figures for the sake of consistencyand clarity.

FIG. 1 is a two-dimensional polar chart of a Lambertian intensitydistribution;

FIG. 2 is a two-dimensional polar chart of a batwing-type intensitydistribution;

FIG. 3 is a schematic side view of a light transmissive substrate inaccordance with embodiments of the invention;

FIG. 4A is an isometric schematic view of an LED light source and a pairof light transmissive substrates with microstructures;

FIG. 4B is an isometric schematic view of a single microstructure of thesubstrates of FIG. 4A;

FIG. 5A is an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 4Ahaving microstructures with roof angles of 90 degrees;

FIG. 5B is a top view of the three-dimensional polar chart of FIG. 5A;

FIG. 5C is a two-dimensional polar chart of the transferred batwingintensity distribution for the embodiment of FIG. 4A havingmicrostructures with roof angles of 90 degrees;

FIG. 5D is an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 4Ahaving microstructures with roof angles of 85 degrees;

FIG. 5E is a two-dimensional polar chart of the transferred batwingintensity distribution for the embodiment of FIG. 4A with themicrostructures having a refractive index of 1.5 and roof angles of 85degrees;

FIG. 5F is a two-dimensional polar chart of the transferred batwingintensity distribution for the embodiment of FIG. 4A with themicrostructures having a refractive index of 1.6 and roof angles of 85degrees;

FIG. 6A is an isometric schematic view of an LED light source and asingle light transmissive substrate with microstructures in accordancewith an embodiment of the invention;

FIG. 6B is an isometric schematic view of a single microstructure of thesubstrate of FIG. 6A;

FIG. 6C is a top schematic view of the single microstructure of FIG. 6B;

FIG. 7A illustrates an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 6Ahaving microstructures with roof angles of 90 degrees;

FIG. 7B illustrates a top view of the three-dimensional polar chart ofFIG. 7A;

FIG. 7C illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 6A with themicrostructures having a refractive index of 1.5 and roof angles of 90degrees;

FIG. 7D illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 6A with themicrostructures a refractive index of 1.6 and roof angles of 90 degrees;

FIG. 7E illustrates an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 6Ahaving microstructures with roof angles of 80 degrees;

FIG. 7F illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 6A havingmicrostructures with roof angles of 80 degrees;

FIG. 7G illustrates an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 6Ahaving microstructures with roof angles of 70 degrees;

FIG. 7H illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 6A havingmicrostructures with roof angles of 70 degrees;

FIG. 7I illustrates an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 6Ahaving microstructures with roof angles of 60 degrees;

FIG. 7J illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 6A havingmicrostructures with roof angles of 60 degrees;

FIG. 7K illustrates an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG. 6Ahaving microstructures with roof angles of 100 degrees;

FIG. 7L illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 6A havingmicrostructures with roof angles of 100 degrees;

FIG. 8A is an isometric schematic view of an LED light source and asingle light transmissive substrate with microstructures in accordancewith an embodiment of the invention;

FIG. 8B is an isometric schematic view of a single microstructure of thesubstrate of FIG. 8A;

FIG. 8C is a top schematic view of the single microstructure of FIG. 8B;

FIG. 9A is an isometric view of a transferred batwing intensitydistribution three-dimensional polar chart for the embodiment of FIG.8A;

FIG. 9B is a top view of the three-dimensional polar chart of FIG. 9A;

FIG. 9C is a two-dimensional polar chart of the transferred batwingintensity distribution for the embodiment of FIG. 8A with themicrostructures having a refractive index of 1.5;

FIG. 9D illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 8A with themicrostructures having a refractive index of 1.6;

FIG. 10 is an isometric schematic view of a microstructure in accordancewith an embodiment of the invention;

FIG. 11 is an isometric schematic view of a microstructure in accordancewith an embodiment of the invention;

FIG. 12A illustrates an LED light source and a single light transmissivesubstrate with microstructures in accordance with an embodiment of theinvention;

FIG. 12B illustrates a single microstructure of FIG. 12A;

FIG. 13A illustrates an isometric view of a transferred batwingintensity distribution three-dimensional polar chart for the embodimentof FIG. 12A;

FIG. 13B illustrates a top view of the three-dimensional polar chart ofFIG. 13A;

FIG. 13C illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 12A,

FIG. 14A illustrates an isometric view of a light transmissive substratewith microstructures in accordance with an embodiment of the invention;

FIG. 14B illustrates an isometric view of a transferred batwingintensity distribution three-dimensional polar chart for the embodimentof FIG. 14A;

FIG. 14C illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 14A,

FIG. 15A illustrates an isometric view of a light transmissive substratewith microstructures in accordance with an embodiment of the invention;

FIG. 15B illustrates an isometric view of a transferred batwingintensity distribution three-dimensional polar chart for the embodimentof FIG. 15A;

FIG. 15C illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 15A with themicrostructures having a refractive index of 1.5; and

FIG. 15D illustrates a two-dimensional polar chart of the transferredbatwing intensity distribution for the embodiment of FIG. 15A with themicrostructures having a refractive index of 1.6.

DETAILED DESCRIPTION

Embodiments of the present invention provide light transmissivesubstrates having microstructures that may provide the desired effect oftransforming a Lambertian intensity distribution received from a lightsource, such as an LED, into a batwing intensity distribution that hasmaximum intensity away from nadir and at about ±30° to about ±60° from Xand Y axes, and minimum intensity at nadir.

FIG. 3 is a schematic illustration of a light transmissive substrate 100for transforming a Lambertian light distribution into a batwing lightdistribution in accordance with embodiments of the invention. Thesubstrate 100 includes a first surface 110 that includes a plurality ofmicrostructures 112, and a second surface 120 on a side of the substrate100 opposite the first surface 110.

As discussed in further detail below, the substrate 100 is configured toreceive light in a Lambertian distribution from a light source at thefirst surface 110 and transform the light into a batwing distributionexiting the second surface 120. The resulting batwing distributiondesirably has a peak intensity in a range of about ±30° to about ±60°from X and Y axes and a minimum intensity at nadir. In an embodiment,the light transmissive substrate 100 may provide a batwing distributionthat has a peak intensity at about ±45 from X and Y axes and a minimum(near zero) intensity at nadir. In some embodiments of the invention, atleast the light transmissive microstructures are made from a materialhaving a refractive index of about 1.5, although materials havingdifferent refractive indices may also be used as long as the desiredeffect can be achieved. In some embodiments of the invention, the restof the substrate is a film made of a material that also has a refractiveindex of about 1.5, or a refractive index that matches or substantiallymatches the refractive index of the microstructures. For light sourcesthat emit infrared beams, infrared transmitting materials that may notbe transparent in the visible range of light may be used. Variousembodiments of the invention are described in further detail below.

FIG. 4A illustrates two light transmissive substrates 400A, 400B, eachhaving a plurality of microstructures 412 on first surfaces 410A, 410Bthereof, that are oriented orthogonally to each other and placed above alight source 430 that outputs light in a Lambertian distribution. Thefirst surfaces 410A, 410B of the light transmissive substrates 400A,400B are oriented towards the light source 430 and second surfaces 420A,420B of the substrates 400A, 400B are oriented away from the lightsource 430. FIG. 4B illustrates a single microstructure 412 in furtherdetail. As illustrated, the microstructure 412 is in the form of a ridgethat has a so-called roof angle or vertex a (see FIG. 3) of 90 degrees.

Light emitting from the light source 430 enters the first substrate 400Aclosest to the light source 430 via its first surface 410A, exits thefirst substrate 400A at its second surface 420A, enters the secondsubstrate 400B at its first surface 410B, and exits the second substrate400B at its second surface 420B. The different orientations of themicrostructures 412 (i.e. being substantially perpendicular to eachother) cause the light to bend and spread in two different directionsand result in a net spread that is that is stronger and in a differentdirection relative to X and Y axes than if only one of the lighttransmissive substrates 400A, 400B is used.

FIGS. 5A-5C illustrate three dimensional and two-dimensionalrepresentations of the light distribution provided by the combination ofthe two light transmissive substrates 400 having a refractive index of1.5 and arranged as illustrated in FIG. 4A. As illustrated, light energyis not only steered away from the 0 degree (nadir) emitting direction,but also pushed toward four directions approximately 45 degrees from theprimary X and Y axes as shown in FIGS. 5A and 5B. Along thosedirections, light typically travels the longest path length reaching thetarget area where stronger intensity is desired. Such a distribution maybe desirable when there are multiple light sources arranged in asubstantially square array, such as in back-lit displays or large arealighting applications (such as when lighting a warehouse). FIG. 5C is a2D polar plot of the light intensity distributions represented by FIGS.5A and 5B.

The prism angles α on both substrates 400 may be adjusted to optimizethe output distribution. For example, in an embodiment, the roof angle αof the ridges 412 on the substrates 400 may be 85 degrees. FIG. 5Dillustrates a three dimensional representation of the light distributionprovided by the combination of the two light transmissive substrates 400having a refractive index of 1.5 with the ridges 412 having a roofangles of 85 degrees, and arranged as illustrated in FIG. 4A. FIG. 5E isa 2D polar plot of the light intensity distribution represented by FIG.5D. FIG. 5F is a 2D polar plot of the light intensity distributionprovided by the combination of the two light transmissive substrates 400having a refractive index of 1.6 with the ridges 412 having a roofangles of 85 degrees, and arranged as illustrated in FIG. 4A. Acomparison of FIGS. 5E and 5F shows the influence the refractive indexhas on the batwing spreading performance of the substrates.

Textures may be added to the second surface 420 of either or bothsubstrates to fine tune the distribution profile and to enhance theoptical transmission efficiencies.

FIG. 6A illustrates an embodiment of a light transmissive substrate 600that has a plurality of microstructures 612 on a first surface 610thereof. In this embodiment, the microstructures 612 are in the form ofan array of micro-pyramids, each having four faces, that are placedabove an LED light source 630 that outputs light in a Lambertiandistribution. As depicted in FIG. 6A, the light enters the substrate 600via the first surface 610 having the array of micro-pyramids 612 andexits a second surface 620 on an opposite side of the substrate 600 asthe first surface 610. Each of the microstructures 612 has a roof angleα (see FIG. 3) of 90 degrees, and is shown in further detail in FIGS. 6B(perspective view) and 6C (top view). Pyramid roof angles may beadjusted to optimize the output distribution, and textures may be addedto the second surface 620 of the substrate 600 to fine tune thedistribution profile and to enhance the optical transmissionefficiencies.

A representation of the three dimensional transformation of the lightdistribution provided by the substrate 600 having a refractive index of1.5 is shown in FIGS. 7A and 7B. In this embodiment, light energy is notonly steered away from the 0 degree emitting direction, but also pushedtoward four directions approximately 45 degrees from the primary X and Yaxes as shown. Along those directions, light typically travels thelongest path length reaching the target area where stronger intensity isdesired. FIG. 7C is a 2D polar plot of the light intensity distributionsrepresented by FIGS. 7A and 7B.

FIG. 7D is a 2D polar plot of a representation of the light intensitydistribution provided by the substrate 600 having a refractive index of1.6 with the micro-pyramids having a roof angle α of 90 degrees. Acomparison of FIGS. 7C and 7D shows the influence the refractive indexhas on the batwing spreading performance of the substrate 600.

The roof angle α of the micro-pyramids 612 affects the lightdistribution provided by the substrate 600 having a refractive index of1.5, as illustrated by FIGS. 7A-7C and 7E-7L. As illustrated, roofangles α of 80 degrees (represented by FIGS. 7E and 7F) and 70 degrees(represented by FIGS. 7G and 7H) as compared to 90 degrees (representedby FIGS. 7A-7C) provide different zero degree light intensities as wellas shapes of the batwing distribution. Roof angles α of 60 degrees(represented by FIGS. 71 and 7J) and 100 degrees (represented by FIGS.7K and 7L) provide different zero degree light intensities, but do notprovide batwing distributions. According to embodiments of theinvention, the roof angle α of the micro-pyramids 612 is in the range of70 degrees to 95 degrees for substrates having a refractive index of1.5.

FIG. 8A illustrates a light transmissive substrate 800 that has an arrayof microstructures 812 on a first surface 810 thereof. In thisembodiment, the microstructures 812 are in the form of an array ofhybrid micro-pyramids that are placed above an LED light source 830 thatoutputs light in a Lambertian distribution. As illustrated in FIG. 8A,the light enters the substrate 800 via the first surface 810 having thearray of hybrid micro-pyramids 812 and exits a second surface 820 on anopposite side of the substrate 800 as the first surface 810. FIGS. 8Band 8C illustrate the hybrid micro-pyramid 812 in further detail. Asillustrated, a top portion 814 of the hybrid micro-pyramid 812 may havea roof angle α (see FIG. 3) of 85 degrees, and a bottom portion(frustum) 816 of the hybrid micro-pyramid 812 may have a roof angle α of70 degrees. In embodiments in which the roof angle α of the bottomportion 816 is 70 degrees, sides 818 of the bottom portion 816 are eachdisposed at an angle β (see FIG. 3) of 55 degrees. In an embodiment, thetop portion 814 may have a roof angle α of between 85 degrees and 90degrees.

A representation of the three dimensional transformation of the lightdistribution provided by the substrate 800 having a refractive index of1.5 is shown in FIGS. 9A and 9B. As illustrated, the hybridmicro-pyramid may provide enhanced performance when compared to a“simple” pyramid, such as the pyramid 612 described above. In thisembodiment, light energy is not only steered farther away from the 0degree emitting direction, but also pushed toward four directionsapproximately 45 degrees from the primary X and Y axes as shown. Alongthose directions, light typically travels the longest path lengthreaching the target area where stronger intensity is desired. FIG. 9C isa 2D polar plot of the light intensity distributions represented byFIGS. 9A and 9B.

FIG. 9D is a 2D polar plot of a representation of the light intensitydistribution provided by the substrate 800 having a refractive index of1.6 with the hybrid micro-pyramids 812 having the top portion 814 with aroof angle α (see FIG. 3) of 85 degrees, and the bottom portion 816 witha roof angle α of 70 degrees. A comparison of FIGS. 9C and 9D shows theinfluence the refractive index has on the batwing spreading performanceof the substrate 600.

Pyramid roof angles α for the top portion 814 and the bottom portion 816may be adjusted to optimize the output distribution. Textures may beadded to the second surface 820 of the substrate 800 to fine tune thedistribution profile and to enhance the optical transmissionefficiencies. Although FIGS. 9A-9C illustrate a hybrid pyramid that hastwo portions and sharp edges and transitions between the two portions,it is contemplated that the hybrid pyramid may have more than twoportions and/or facets of the hybrid pyramid may be curved, therebyadding flexibilities for further transformation fine tuning andperformance optimizations. For example, FIG. 10 illustrates athree-section hybrid micro-pyramid 1000 that may be used for themicrostructure 812 of FIG. 8A, and FIG. 11 illustrates a curved-facethybrid micro-pyramid 1100 that may be used for the microstructure 812 ofFIG. 8A.

FIG. 12A illustrates a light transmissive substrate 1200 that has anarray of microstructures 1212 on a first surface 1210 thereof. In thisembodiment, the microstructures 1212 are in the form of an array of“folded” micro-pyramids that are placed above an LED light source 1230that outputs light in a Lambertian distribution. As illustrated in FIG.12A, the light enters the substrate 1200 via the first surface 1210having the array of folded micro-pyramids 1212 and exits a secondsurface 1220 on an opposite side of the substrate 1200 as the firstsurface 1210. FIG. 12B illustrates the folded micro-pyramid 1212 infurther detail. As illustrated, the folded micro-pyramid has a frustumor base section 1214 and a recess 1216 having the shape of amicro-pyramid in the base section 1214, thereby giving the pyramid aconfiguration that looks as though the tip of a simple pyramid waspressed downward and into the base section 1214 or “folded” into thebase section 1214. Both the base section 1214 and the recess 1216 mayhave roof angles α (see FIG. 3) of 90 degrees.

Folded pyramids may enhance the manufacturability of the lighttransmissive substrate to overcome a restriction on the height of themicrostructures in the Z-direction (represented by ‘h’ in FIG. 3) formany microstructure fabrication processes. Folded pyramids also offerpossibilities of achieving functionalities of structures of largerheights (h in FIG. 3) than the fabrication process may allow. In anembodiment, the height h of the microstructures may be in the range ofabout 10 micrometers to about 50 micrometers. Pyramid roof angles may beadjusted to optimize the output distribution. Textures may be added tothe second surface 1220 of the substrate 1200 to fine tune thedistribution profile and to enhance the optical transmissionefficiencies.

A representation of the three dimensional transformation of the lightdistribution provided by the substrate 1200 is shown in FIGS. 13A and13B. In this embodiment, light energy is not only steered away from the0 degree emitting direction, but also pushed toward four directionsapproximately 45 degrees from the primary X and Y axes as shown. Alongthose directions, light typically travels the longest path lengthreaching the target area where stronger intensity is desired. FIG. 13Cis a 2D polar plot of the light intensity distributions represented byFIGS. 13A and 13B.

FIG. 14A illustrates an embodiment of a light transmissive substrate1400 with an array of microstructures 1412 in the form of corner cubeshaving square shaped faces that may be used in place of the lighttransmissive substrates described above. A representation of the threedimensional transformation of the light distribution provided by thesubstrate having a refractive index of 1.5 and the microstructures 1412is shown in FIG. 14B. FIG. 14C is a 2D polar plot of the light intensitydistribution represented by FIG. 14B.

FIG. 15A illustrates an embodiment of a light transmissive substrate1500 with an array of microstructures 1512 in the form of corner cubeshaving triangular shaped faces. A representation of the threedimensional transformation of the light distribution provided by themicrostructures 1512 having a refractive index of 1.5 is shown in FIG.15B. FIG. 15C is a 2D polar plot of the light intensity distributionrepresented by FIG. 15B.

FIG. 15D is a 2D polar plot of a representation of the light intensitydistribution provided by the microstructures 1512 having a refractiveindex of 1.6. A comparison of FIGS. 15C and 15D shows the influence therefractive index has on the batwing spreading performance of thesubstrate 1500.

The light transmissive structures according to any of the embodimentsdescribed herein may be created using many techniques known in the art.For example, in an embodiment, the shape of the microstructures may becast onto a substrate using a suitable master mold, and thermally-curingpolymer or ultraviolet (UV) light curing polymer, or the shape may beimpressed into a thermoplastic substrate through compression molding orother molding, or may be created at the same time as the substrate usingextrusion-embossing or injection molding. The microstructures may beproduced by replicating a master. For example, an optical diffuser maybe made by replication of a master containing the desired shapes asdescribed in U.S. Pat. No. 7,190,387 B2 to Rinehart et al., entitled“Systems And Methods for Fabricating Optical Microstructures Using aCylindrical Platform and a Rastered Radiation Beam”; U.S. Pat. No.7,867,695 B2 to Freese et al., entitled “Methods for MasteringMicrostructures Through a Substrate Using Negative Photoresist”; and/orU.S. Pat. No. 7,192,692 B2 to Wood et al., entitled “Methods forFabricating Microstructures by Imaging a Radiation Sensitive LayerSandwiched Between Outer Layers”, assigned to the assignee of thepresent invention, the disclosures of all of which are incorporatedherein by reference in their entirety as if set forth fully herein. Themasters themselves may be fabricated using laser scanning techniquesdescribed in these patents, and may also be replicated to providediffusers using replicating techniques described in these patents.

In an embodiment, laser holography, known in the art, may be used tocreate a holographic pattern that creates the desired microstructures ina photosensitive material. In an embodiment, projection or contactphotolithography, such as used in semiconductor, display, circuit board,and other common technologies known in the art, may be used to exposethe microstructures into a photosensitive material. In an embodiment,laser ablation, either using a mask or using a focused and modulatedlaser beam, may be used to create the microstructures including theindicia in a material. In an embodiment, micromachining (also known asdiamond machining), known in the art, may be used to create the desiredmicrostructures from a solid material. In an embodiment, additivemanufacturing (also known as 3D printing), known in the art, may be usedto create the desired microstructure in a solid material.

For any of the embodiments of the light transmissive substrate describedherein, roof angles of the microstructures may be adjusted, and ortextures may be added to the second surface of the substrate to finetune the distribution profile and to enhance the optical transmissionefficiencies. As described above, the refractive index of themicrostructures also has an influence on the batwing spreadingperformance and may be adjusted to optimize performance.

The embodiments described herein represent a number of possibleimplementations and examples and are not intended to necessarily limitthe present disclosure to any specific embodiments. Instead, variousmodifications can be made to these embodiments, and differentcombinations of various embodiments described herein may be used as partof the invention, even if not expressly described, as would beunderstood by one of ordinary skill in the art.

For example, although four-sided pyramids have been described, it iscontemplated that other geometries, such as microstructures having 3, 5or 6 sides or circular (cone) geometries may be used. Also, it iscontemplated that the surfaces of the microstructures may havevariations and either in a pattern or random variations or combinationsthereof. In some embodiments, the microstructures may have asymmetricalinstead of symmetrical shapes and arrays of microstructures may includemicrostructures having different shapes and/or sizes, either in apattern or random variations or combinations thereof. Any suchmodifications are intended to be included within the spirit and scope ofthe present disclosure and protected by the following claims.

1-11. (canceled)
 12. A light transmissive substrate for transforming aLambertian light distribution into a batwing light distribution, thelight transmissive substrate comprising: a first surface comprising aplurality of microstructures; and a second surface on a side of thesubstrate opposite the first surface, wherein each of the plurality ofmicrostructures has a shape of a pyramid with a roof angle of betweenabout 70° and about 95° and extending in a direction away from thesecond surface, wherein the substrate is configured to receive light ina Lambertian distribution from a light source at the first surface andtransform the light into a three-dimensional batwing distributionexiting the second surface, the three-dimensional batwing distributionhaving peak intensities at angles ranging from ±30° to about ±60° from Xand Y axes and a desired intensity at nadir that is less than at leastone of peak intensities and, wherein a refractive index of themicrostructures and the roof angle are chosen to provide a desired shapeof the three-dimensional batwing distribution and the desired intensityat nadir.
 13. The light transmissive substrate according to claim 12wherein the refractive index of the microstructures is chosen to be in arange of 1.5 to 1.6.
 14. The light transmissive substrate according toclaim 12 wherein the roof angle is chosen to be in a range of 70° and95°.
 15. The light transmissive substrate according to claim 12 whereinthe refractive index of the microstructures is chosen so the desiredintensity at nadir is substantially zero.
 16. The light transmissivesubstrate according to claim 12 wherein the roof angle is chosen so thedesired intensity at nadir is substantially zero
 17. The lighttransmissive substrate according to claim 12 wherein the refractiveindex of the microstructures is chosen so the desired intensity at nadiris greater than zero and less than at least one of the peak intensity atabout ±30° to about ±60° from X and Y axes.
 18. The light transmissivesubstrate according to claim 12 wherein the roof angle is chosen so thedesired intensity at nadir is greater than zero and less than at leastone of the peak intensity at about ±30° to about ±60° from X and Y axes.19. The light transmissive substrate according to claim 12 wherein therefractive index of the microstructures and the roof angle are chosensuch that the refractive index is 1.5 and the roof angle is in a rangeof 70° and 95°.
 20. The light transmissive substrate according to claim12 wherein the refractive index of the microstructures and the roofangle are chosen such that the refractive index is 1.6 and the roofangle is substantially 90°.
 21. The light transmissive substrateaccording to claim 12 wherein each of the at least one microstructurecomprises a pyramid having a base portion and a top portion connected tothe base portion, wherein the top portion comprises a tip of the pyramidand sides disposed at different angles compared with sides of the baseportion.
 22. The light transmissive substrate according to claim 12wherein each of the at least one microstructure comprises athree-section hybrid pyramid.
 23. The light transmissive substrateaccording to claim 12 wherein each of the at least one microstructurecomprises a curved-facet-section hybrid pyramid.
 24. The lighttransmissive substrate according to claim 12 wherein each of the atleast one microstructure comprises a folded micro-pyramid.
 25. A lighttransmissive substrate for transforming a Lambertian light distributioninto a batwing light distribution, the substrate comprising: a firstsubstrate comprising a first surface comprising a plurality ofmicrostructures, at least one of the plurality of microstructuresforming a ridge having a first roof angle and the first substratefurther comprising a second surface parallel to the first surface; and asecond substrate comprising a first surface comprising a plurality ofmicrostructures, at least one of the plurality of microstructuresforming a ridge having a second roof angle and the second substratefurther comprising a second surface parallel to the first surface thefirst substrate, wherein the first and second substrates are positionedsuch that the second substrate is oriented substantially orthogonallywith respect to the first substrate and configured such that light in aLambertian distribution from a light source enters the first substratepositioned closest to the light source via the first surface of thefirst substrate, exits the first substrate at the second surface of thefirst substrate, enters the second substrate at the first surface of thesecond substrate, and exits the second substrate at the second surfaceof the second substrate, the light exiting the second surface of thesecond substrate being transformed into a batwing distribution havingpeak intensities at angles ranging from ±30° to about ±60° from X and Yaxes and a desired intensity at nadir that is less than at least one ofthe peak intensities and wherein a refractive index of microstructuresin at least one of the first and second substrate and at least one ofthe first and second roof angle are chosen to provide a desired shape ofthe three-dimensional batwing distribution and the desired intensity atnadir.
 26. The light transmissive substrate according to claim 25wherein the first and second roof angles are equal.
 27. The lighttransmissive substrate according to claim 25 wherein at least one of thefirst and second roof angle is in a range between about 70° and about95°.
 28. The light transmissive substrate according to claim 25 whereinthe refractive index of microstructures in at least one of the first andsecond substrate is chosen to be 1.5.
 29. The light transmissivesubstrate according to claim 25 wherein the refractive index ofmicrostructures in at least one of the first and second substrate ischosen to be in a range of 1.5 to 1.6.
 30. The light transmissivesubstrate according to claim 25 wherein the refractive index ofmicrostructures in at least one of the first and second substrate and atleast one of the first and second roof angle are chosen so the desiredintensity at nadir is substantially zero.
 31. The light transmissivesubstrate according to claim 25 wherein the refractive index of at leastone of the first and second substrate and the refractive index of atleast one of the first and second roof angle are chosen so the desiredintensity at nadir is greater than zero and less than at least one ofthe peak intensities.
 32. The light transmissive substrate according toclaim 25 wherein the refractive index of microstructures in at least oneof the first and second substrate and at least one of the first andsecond roof angle are chosen such that the desired shape of thethree-dimensional batwing distribution and the desired intensity atnadir comprise a batwing distribution having peak intensities at anglesof about ±45° from X and Y axes and substantially zero intensity atnadir.
 33. The light transmissive substrate according to claim 32wherein the refractive index of microstructures in at least one of thefirst and second substrate is 1.5.
 34. The light transmissive substrateaccording to claim 32 wherein the refractive index of microstructures inat least one of the first and second substrate is 1.6 and at least oneof the first and second roof angle are 85°.
 35. The light transmissivesubstrate according to claim 25 wherein the desired shape of thethree-dimensional batwing distribution has peak intensities at angles ofabout ±55° from X and Y axes.
 36. The light transmissive substrateaccording to claim 25 wherein at least one of the second surface of thefirst substrate and the second surface of the second substrate comprisesa textured surface.